Isn't ridiculously powerful private armies one of the big reasons the Roman Republic turned into a dictatorship?
I'm personally in favor of dramatically reducing the size of the US military, by any arbitrary percent, but this is a stupid and dangerous way to do it. NGOs should not have militaries.
The way I see it, the world powers are already incapable, and unwilling, engage in direct armed conflict with each other. We proved that in the cold war. At best it would be a repeat of the first world war, at worst it would be nuclear armageddon. With that in mind it seems like folly to maintain early 20th century standing armies. We're never going to use them for anything more than small-scale engagements and military occupations (i.e. Russia in Ukraine, China in Tibet, the US in Iraq), but our militaries are based on the idea of an impossible conflict between the giants. It's silly and paranoid.
Western nations are downsizing their militaries quite a bit, and the overall size is already tiny compared to WWII numbers; the USAAF had in excess of 50,000 aircraft relative to today's 5,000. The F-35 and LCS are good examples of this new cost saving mentality; mission versatility and interoperability built in to an already cheap platform, which then replaces the bigger and purpose built platforms of old.
There's also been plenty of news stories published in recent months regarding the capability of individual forces within NATO (i.e the Bundeswehr training with broomsticks instead of rifles, Luftwaffe Typhoon's not being ready, etc). Russia, too, has shown its lack of readiness in the consistent aircraft hull losses driven by a heightened state of readiness brought on by the Ukraine crisis. There just isn't the military spending that there used to be, and it shows.
I also disagree that a conflict similar to WWI would ever take place again. What distinguished WWI was trench warfare, which was largely dictated by the immobile nature of warfare at that time and the superiority of defensive tools like the machine gun. Modern technology means an entirely different battlefield if such large scale combat were to take place again. I wouldn't be surprised if conflict between nation states fizzled out quickly on account of quick losses in expensive hardware, such as aircraft or ships. It's all well and good for rebels to blow up a few old T-72's in disparate regional conflicts, but how many T-90 losses could Russia stomach? How many F-16's could the US stand to lose?
Finally, conflict between the big boys doesn't necessarily mean Armageddon. From memory, Russia always planned the use of tactical nuclear strikes in the case of hypothetical conflict with NATO. I doubt such an attack would spark global nuclear warfare. MAD just means nation states are unlikely to nuke each other, not that they won't enter conflict at all.